The concepts ofπ-irreduciblity,recurrence and transience are introduced into the research field of Markov chains in random environments.That aπ-irreducible chain must be either recurrent or transient is proved,a cri...The concepts ofπ-irreduciblity,recurrence and transience are introduced into the research field of Markov chains in random environments.That aπ-irreducible chain must be either recurrent or transient is proved,a criterion is shown for recurrent Markov chains in double-infinite random environments,the existence of invariant measure ofπ-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.展开更多
基金the Natural Science Foundation of Hunan Province(Grant No.99JJY2001)Hunan Provincial Foundation for Young and Middleaged People(Grant No.00JJEY2141).
文摘The concepts ofπ-irreduciblity,recurrence and transience are introduced into the research field of Markov chains in random environments.That aπ-irreducible chain must be either recurrent or transient is proved,a criterion is shown for recurrent Markov chains in double-infinite random environments,the existence of invariant measure ofπ-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.
